In the Faiths & Philosophies book, there's a feat that gives you an animal companion at your level - 3. It has a prerequisite, so it'll cost you two feats (and you may want to spend a third on Boon Companion to get it up to your level), but it is an option.
Depending on your deity, you maybe be able to retrain into the Animal domain to get access to an animal companion as a class feature.
The best option, though, is probably to GM those 3 scenarios yourself, and put the credit on a brand-new character who is built from the ground up to use the Axe Beak.
If it's the scenario I think it is, the axe beak is not available through GM credit (bizarre, but yeah). You can GM the first two of the three, but the last one has to be a character who plays the scenario.
He could GM enough to get a star, including the first two, and then use his star replay for that scenario, and use the same character to which he assigned GM credit for the first two parts of the arc.
I'm assuming this is for your Tengu Inquisitor you have listed as a PFS character. If the profile is accurate, Andoletta wouldn't allow animal as a domain, so either the Faiths and Philosophies option, or multiclassing, would be the best option. A Cavalier or Samurai could work, and a properly chosen order would fit with the theme of the deity.
If it's the scenario I think it is, the axe beak is not available through GM credit (bizarre, but yeah).
Huh? How do you figure? GMs can take any boons they want from the chronicle when they get their credit.